Low tensor train and low multilinear rank approximations of 3D tensors for compression and de-speckling of optical coherence tomography images

Abstract

Objective. Many methods for compression and/or de-speckling of 3D optical coherence tomography (OCT) images operate on a slice-by-slice basis and, consequently, ignore spatial relations between the B-scans. Thus, we develop compression ratio (CR)-constrained low tensor train (TT)—and low multilinear (ML) rank approximations of 3D tensors for compression and de-speckling of 3D OCT images. Due to inherent denoising mechanism of low-rank approximation, compressed image is often even of better quality than the raw image it is based on. Approach. We formulate CR-constrained low rank approximations of 3D tensor as parallel non-convex non-smooth optimization problems implemented by alternating direction method of multipliers of unfolded tensors. In contrast to patch- and sparsity-based OCT image compression methods, proposed approach does not require clean images for dictionary learning, enables CR as high as 60:1, and it is fast. In contrast to deep networks based OCT image compression, proposed approach is training free and does not require any supervised data pre-processing. Main results. Proposed methodology is evaluated on twenty four images of a retina acquired on Topcon 3D OCT-1000 scanner, and twenty images of a retina acquired on Big Vision BV1000 3D OCT scanner. For the first dataset, statistical significance analysis shows that for CR ≤ 35, all low ML rank approximations and Schatten-0 (S 0) norm constrained low TT rank approximation can be useful for machine learning-based diagnostics by using segmented retina layers. Also for CR ≤ 35, S 0-constrained ML rank approximation and S 0-constrained low TT rank approximation can be useful for visual inspection-based diagnostics. For the second dataset, statistical significance analysis shows that for CR ≤ 60 all low ML rank approximations as well as S 0 and S 1/2 low TT ranks approximations can be useful for machine learning-based diagnostics by using segmented retina layers. Also, for CR ≤ 60, low ML rank approximations constrained with S p , p ∊ {0, 1/2, 2/3} and one surrogate of S 0 can be useful for visual inspection-based diagnostics. That is also true for low TT rank approximations constrained with S p , p ∊ {0, 1/2, 2/3} for CR ≤ 20. Significance. Studies conducted on datasets acquired by two different types of scanners confirmed capabilities of proposed framework that, for a wide range of CRs, yields de-speckled 3D OCT images suitable for clinical data archiving and remote consultation, for visual inspection-based diagnosis and for machine learning-based diagnosis by using segmented retina layers.